Embodiments of the present invention generally relate to the determining information about targets using signals produced by a sensor system, and more specifically, obtaining target dimensions having extents which are smaller that the collected resolution supported by the bandwidth of the sensor system, using deconvolution techniques.
Conventional sensor systems theory states that the degree to which a target can be resolved in the direction of signal propagation is typically dependent upon the bandwidth of the sensor system. The direction of signal propagation is hereinafter referred to as the range direction. The smallest dimension that can be resolved in range can be referred to as the range resolution. In one example, when the sensor system is a radar system, a radar receiver can perceive the target as a collection of resolution cells. Each resolution cell can be thought of as a discrete unit of area having a size dependent upon the range resolution. As the resolution cell becomes finer (i.e., smaller), greater detail can be derived from the radar returns received from a target.
FIG. 1 is an idealized diagram illustrating the relationship between bandwidth and range resolution for an exemplary radar system. A radar 102 transmits a transmit signal xT(t). In this example, xT(t) presented as a signal having a simple pulse waveform for ease of explanation; however, one of ordinary skill in the art would appreciate these concepts hold true for waveforms using any known modulation type and/or coding. For simple pulses, the bandwidth of the pulse signal, BW (typically measured in Hz), is inversely proportional to the pulse length τ (typically measured in sec). Additionally, while only one pulse is shown for ease of explanation, a plurality of transmit pulses can be sequentially transmitted at a periodic rate known as the Pulse Repetition Frequency (PRF). Once transmitted from radar 102, transmit signal xT(t) propagates through space until it strikes a target 104. Target 104 is illustrated as having three major facets (or reflectors) separated in the range direction, each of which reflect some portion of energy supplied by transmit signal xT(t) back toward radar 102. Radar 102 is configured to receive the three reflected pulses, which are designated as receive signals xR1(t), xR2(t), and xR3(t). Each received signal xR1(t), xR2(t), and xR3(t) is received by radar 102 at different times. The time of reception depends upon the distance between each feature of target 104 and radar 102.
Further referring to FIG. 1, two graphs are illustrated depicting transmit signal xT(t) and receive signals xR1(t), xR2(t), and xR3(t) for transmit pulses having different bandwidths. The vertical axes represent amplitude and the horizontal axes represent time. A first graph 106 represents a scenario where the transmit signal x1T(t) has a narrow pulse width τN, and therefore a corresponding wide bandwidth. Receive signals x1R1(t), x1R2(t), and x1R3(t), each also having a narrow pulse width, are distinct and can be easily distinguished by radar 102. Using a transmit signal having pulse width τN, the three features on target 104 can be separately resolved and separate measurements can be performed with respect to each feature. Therefore, the transmitted signal having the narrow pulse width can resolve smaller features in range, and thus afford radar 102 with a finer range resolution.
In contrast, second graph 108 depicts a scenario where a transmit signal x2T(t) has a wide pulse width τw, thus having a narrow bandwidth. Receive signals x2R1(t), x2R2(t), and x2R3(t), each also having a wide pulse width, overlap each other to some degree and are indistinguishable by radar 102. As a result, the three features on target 104 can not be separately resolved, so the amount of information radar 102 can extract regarding target 104 is reduced from that in the wide bandwidth case. Because of the coarser resolution of the received signals x2R1(t), x2R2(t), and x2R3(t), separate measurements based upon the three range features of object 104 can not be performed, and the amount of information which can be extracted using the low bandwidth receive pulses can be reduced.
From the two scenarios described above in FIG. 1, it is clear that the amount of bandwidth used in the transmitted signal can be a limiting factor in a radar system's resolution, and hence can limit the information that can be derived regarding the target. Sophisticated signal processing techniques have been established in an attempt to work around bandwidth limitations, such as, for example, bandwidth extrapolation processing and/or modeling techniques such as Multiple Signal Classification (MUSIC). However, these methods can be computationally intensive and may not be suitable in situations where execution time is critical and solutions need to be determined quickly. Moreover, many of these techniques may make assumptions about the underlying structure of the radar signal, or make other simplifying assumptions, that could limit the accuracy of the measurements derived from the received radar signals.